Main reference:
Time-domain analysis - understanding of signal
time-domain analysis methods (crest factor, pulse factor, margin factor, kurtosis factor, shape factor and skewness, etc.) The important notes are as follows
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It is recommended to follow See the reference notes synchronously.
There are 8 dimensional eigenvalues—maximum value, minimum value, peak-to-peak value, mean value, variance, standard deviation, mean square value, root mean square value (RMS) and 6 dimensionless eigenvalues—kurtosis, skewness
, Shape factor, crest factor, pulse factor, margin factor
5 frequency domain eigenvalues - center of gravity frequency, mean square frequency, root mean square frequency, frequency variance, frequency standard deviation
4 spectral kurtosis features - spectrum kurtosis Mean, standard deviation of spectral kurtosis, skewness of spectral kurtosis, kurtosis of spectral kurtosis
(several other related features - other commonly used and uncommonly used feature indicators will be added later)
1. Dimensional eigenvalues
- Dimensional eigenvalues: Dimensional eigenvalues often have intuitive physical meanings and are the most commonly used characteristic indicators. Dimensional eigenvalues mainly include: maximum value, minimum value, peak-to-peak value, mean value, variance, standard deviation, mean square value, root mean square value (RMS), mean square error (MSE), root mean square error (RMSE) , square root amplitude, etc.
- The root mean square represents the energy of the signal
- Variance, which represents the degree of dispersion of the data (signal)
- In a physical sense, the mean square represents the energy of the signal , the expected square represents the DC component of the signal , and the variance represents the AC component of the signal.
- Standard deviation: Both variance and standard deviation indicate the degree of dispersion of the data, so since there is variance, why do we need standard deviation? In order to unify the dimension with the original signal.
For example, suppose the annual average temperature in Beijing is 20°C and the standard deviation is 10°C; the annual average temperature in Urumqi is 20°C and the standard deviation is 15°C. This will give an intuitive understanding of the degree of dispersion of the temperature, but if the variance of the temperature in Beijing is 100 and that in Urumqi is 225, it is very inconvenient to understand. - Mean square error: The
mean square error MSE can evaluate the degree of change (deviation) of the data. The smaller the value of MSE (comparison with each other, rather than comparison with the true value of the parameter), it means that the prediction model has better description of the experimental data. Accuracy.
Excerpt from: https://zhuanlan.zhihu.com/p/57153601
2 Dimensionless features
In summary: the physical meanings of crest factor, pulse factor and margin factor are similar. Both crest factor and pulse factor are used to detect whether there is an impact in the signal. Margin factor is often used to detect the wear and tear of mechanical equipment. The kurtosis factor is also a response to the shock characteristics of the vibration signal, but the expression of the formula is quite different from the first three.
Skewness: Skewness is also called skewness and skewness. There is a certain correlation between skewness and kurtosis. Kurtosis is the ratio of the fourth-order central moment to the fourth power of the standard deviation; skewness is the ratio of the third-order central moment to the third power of the standard deviation. Skewness is the same as kurtosis and describes a distribution. If the physical meaning is simply understood, for a unimodal distribution, negative skewness means that the "head" of the distribution line is on the right and the "tail" is on the left; positive skewness is the opposite. See the picture below:
Form Factor: The form factor is the ratio of the effective value (RMS) to the rectified average. In the field of electronics, its physical meaning can be understood as the ratio of DC current to AC current of equal power, and its value is greater than or equal to 1. Speaking of this, you may have discovered that the form factor = pulse factor / crest factor.
